I have both of the O'Reilly bioinformatics
books, "Beginning
Perl for Bioinformatics" and "Developing
Bioinformatics Computer Skills" and may even get around to written
reviews one of these days. If you are already an accomplished programer/Perl
programer neither will teach you much in that department but they can give you
an idea of the sort of biological problems that are out there. "Developing
Bioinformatics Computer Skills" gives a good rounded overview of the
bioinformatics field with details about common programs. It could be worth your
while checking some of the programs out to see the sort of problems people are
working on and to find out what field might interest you. "Beginning
Perl for Bioinformatics" has some simple but useful scripts that can
form a base to your bioinformatics tool kit if you are a beginner or help you
think about using Perl with some of the idiosyncrasies of the biological world.
As you have more experience you may find BioPerl more your cup of tea.

One of the standard biological books is Molecular
Biology of the Cellamazon.com by Bruce Alberts, Dennis Bray (Contributor),
Julian Lewis, Martin Raff, ke Roberts, James D. Watson and I highly recommend
getting your hands on a copy so that you can figure out what the hell the biologist
are talking about. Its clearly written and contains a wealth of basic information.

My background is in Biochemistry although I have since moved to Analytical
Chemistry (Biological mass spectrometry) and now use Perl for data munging,
automating database searching, and reporting as well as many other tasks. Good
luck moving into this exciting field.